What is the limit as x approaches pi/4 of (sin(2x))/(sin(x)tan(x)) ?

The limit as x approaches pi/4 of (sin(2x))/(sin(x)tan(x)) is square root of 2

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limit as x approaches pi/4 of (sin(2x))/(sin(x)tan(x))

x \to \frac{π}{4} lim (\frac{sin ( 2 x )}{sin ( x ) tan ( x )})

2

Decimal

1.41421 \dots

Solution steps

x \to \frac{π}{4} lim (\frac{sin ( 2 x )}{sin ( x ) tan ( x )})

Plug in the value

x = \frac{π}{4}

= \frac{sin ( 2 \cdot \frac{π}{4} )}{sin ( \frac{π}{4} ) tan ( \frac{π}{4} )}

Simplify

\frac{sin ( 2 \cdot \frac{π}{4} )}{sin ( \frac{π}{4} ) tan ( \frac{π}{4} )} : 2

= 2

What is the limit as x approaches pi/4 of (sin(2x))/(sin(x)tan(x)) ?
The limit as x approaches pi/4 of (sin(2x))/(sin(x)tan(x)) is square root of 2